mugenziwzn6

## Answered question

2023-02-21

The permutations and combinations of $abcd$ taken $3$ at a time are respectively.

### Answer & Explanation

Helen House

Beginner2023-02-22Added 10 answers

Step 1. Calculate the permutations.
When n objects are taken into consideration, the number of permutations is given by,
$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$
We have to find permutations of $abcd$ taken $3$ at a time.
$\therefore P\left(4,3\right)=\frac{4!}{\left(4-3\right)!}⇒=\frac{4×3×2×1}{1}⇒=24$
Step 2. Figure out the combination..
The number of combinations of $n$ objects taken $r$ at a time is given by,
$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$
We have to find combinations of $abcd$ taken $3$ at a time.
$\therefore C\left(4,3\right)=\frac{4!}{3!\left(4-3\right)!}=\frac{4×3×2×1}{3×2×1×1}=4$
Hence, the permutation and combination are $24$ and $4$respectively.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?